The Technomancer
card-carrying scientician
One difference would be that private corporations cannot withhold government services as a bargaining chip.
Sure, but what does that have to do with monetary political donations? The way I see it the point where those organizations would be threatening to withhold services comes after the election and is a completely separate issue from their ability to donate unlimited amounts of money to election campaigns. I don't see specifically why the points that you raised against unlimited union contribution can't also be used as arguments for limitations on corporate contribution in the context of holding elections.
Or to put it more concisely: why are the specific points you raised not valid for corporations as well?